0 votes 0 votes Boolean algebra is a bounded distributed complemented lattice, also lattice is a poset thus it satisfies reflexive , antisymmetric and transitive properties. Does Boolean Algebra satisfy commutative law? Mathematical Logic boolean-algebra discrete-mathematics lattice + – Nidhi Budhraja asked Aug 22, 2018 Nidhi Budhraja 828 views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply arvin commented Aug 22, 2018 reply Follow Share yes it does but only for some particular defined relation . not for every relation. say it does well for addition and multiplication but not for division or subtraction. what i mean here is that it will depend upon the satisfiable capacities of the relation for the relation and domain. 0 votes 0 votes Nidhi Budhraja commented Aug 22, 2018 reply Follow Share If Boolean Algebra satisfies commutative law , then how will it satisfy antisymmetric property for being a poset? 0 votes 0 votes arvin commented Aug 22, 2018 reply Follow Share See as far as i am concerned both antisymmetric and commutative properties are different. . We define antisymmetric property for the relation properties. aRb. But to commute i think we can define it over different operations such as *,+,-,/, union ,intersection etc.. See just as Boolean algebra is bounded means 0v1=1v0 its commutative property defined over v. But if u define it over relation it wont satisfy. So i made the statement that it will be dependent on relation and domain. 0 votes 0 votes Nidhi Budhraja commented Aug 22, 2018 reply Follow Share Can you please explain what is meant by each symbol in boolean algebra (B,+,*,',0,1)?which is the operation for which lattice is defined? What do +, *, ', 0, 1 represent here? 0 votes 0 votes arvin commented Aug 22, 2018 reply Follow Share see if we define a relation for <= for every natural number than it will be antisymmetric. as 1<=2 but 2not <=1. so we can define asymmetric behaviour here for the relation. ' but if u define it for + operation it will commute as 1+2=2+1 = 3 and u can find it in the domain of that relation. 1 votes 1 votes smsubham commented Dec 28, 2019 reply Follow Share You should also mention relation wrt which you are asking this. 0 votes 0 votes Please log in or register to add a comment.